Advanced factorization is a gateway to algebraic number theory, which mathematicians study in order to solve famous conjectures like Fermat's Last Theorem.

The polynomial \[9-4x^2-20xy-25y^2\] can be factorized as \((3+ax+by)(3+cx+dy),\) where \(a,\) \(b,\) \(c\) and \(d\) are real numbers. What is the value of \(abcd\)?

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